Inverse Mapping Research Articles

Matrix-Ball Construction of affine Robinson-Schensted correspondence

In his study of Kazhdan-Lusztig cells in affine type A, Shi has introduced an affine analog of Robinson- Schensted correspondence. We generalize the Matrix-Ball Construction of Viennot and Fulton to give a more combi- natorial realization of Shi's algorithm. As a biproduct, we also give a way to realize the affine correspondence via the usual Robinson-Schensted bumping algorithm. Next, inspired by Honeywill, we extend the algorithm to a bijection between extended affine symmetric group and triples (P, Q, ρ) where P and Q are tabloids and ρ is a dominant weight. The weights ρ get a natural interpretation in terms of the Affine Matrix-Ball Construction. Finally, we prove that fibers of the inverse map possess a Weyl group symmetry, explaining the dominance condition on weights.

Performance Enhancement of Optical Comb Based Microwave Photonic Filter by Machine Learning Technique

Machine learning technique is employed to design a microwave photonic filter (MPF) consisting of an optical comb generator and a phase modulator (PM), to realize centralized management of radio signal delivery in optical networks. The proposed comb generator successfully generates up to 103 optical carriers with adjustable wavelength spacing and number of optical carriers. It exhibits large tunability, flat band response and high tone-to-noise ratio. Thus, the proposed optical comb-based filter is capable to provide flexible tunability with respect to its center frequency and 3-dB bandwidth. In our experimental setup, different wavelength spacing settings and number of optical carriers are fed into the PM for modulation and their corresponding frequency responses are measured by a network analyzer. The experimental data have been analyzed to correlate with the simulation results and theoretical predictions. Besides, a subcarrier multiplexing (SCM) technique can be applied to a multi-user optical system incorporating the proposed filter since its frequency response is varied by the accumulated dispersion. After measuring the characteristic of the proposed filter, a set of frequency responses is collected and fed into the convolutional neural network (CNN) model to obtain the inverse mapping between frequency response to the wavelength spacing and fiber length. As a result, the well-trained model can successfully predict the wavelength spacing and fiber length with high accuracy.

Conformal Invariance of CLEΚ on the Riemann Sphere for Κ ∈(4,8)

Abstract The conformal loop ensemble (${\textrm{CLE}}$) is the canonical conformally invariant probability measure on non-crossing loops in a simply connected domain in $\mathbbm{C}$ and is indexed by a parameter $\kappa \in (8/3,8)$. We consider ${\textrm{CLE}}_\kappa $ on the whole-plane in the regime in which the loops are self-intersecting ($\kappa \in (4,8)$) and show that it is invariant under the inversion map $z \mapsto 1/z$. This shows that whole-plane ${\textrm{CLE}}_\kappa $ for $\kappa \in (4,8)$ defines a conformally invariant measure on loops on the Riemann sphere. The analogous statement in the regime in which the loops are simple ($\kappa \in (8/3,4]$) was proven by Kemppainen and Werner and together with the present work covers the entire range $\kappa \in (8/3,8)$ for which ${\textrm{CLE}}_\kappa $ is defined. As an intermediate step in the proof, we show that ${\textrm{CLE}}_\kappa $ for $\kappa \in (4,8)$ on an annulus, with any specified number of inner-boundary-surrounding loops, is well defined and conformally invariant.

Lane-Level Map-Matching Method for Vehicle Localization Using GPS and Camera on a High-Definition Map.

Accurate vehicle localization is important for autonomous driving and advanced driver assistance systems. Existing precise localization systems based on the global navigation satellite system cannot always provide lane-level accuracy even in open-sky environments. Map-based localization using high-definition (HD) maps is an interesting method for achieving greater accuracy. We propose a map-based localization method using a single camera. Our method relies on road link information in the HD map to achieve lane-level accuracy. Initially, we process the image—acquired using the camera of a mobile device—via inverse perspective mapping, which shows the entire road at a glance in the driving image. Subsequently, we use the Hough transform to detect the vehicle lines and acquire driving link information regarding the lane on which the vehicle is moving. The vehicle position is estimated by matching the global positioning system (GPS) and reference HD map. We employ iterative closest point-based map-matching to determine and eliminate the disparity between the GPS trajectories and reference map. Finally, we perform experiments by considering the data of a sophisticated GPS/inertial navigation system as the ground truth and demonstrate that the proposed method provides lane-level position accuracy for vehicle localization.

An Inverse Mapping Table Method for Raindrop Size Distribution Parameters Retrieval Using X-band Dual-Polarization Radar Observations

An inverse mapping table (IMT) method is proposed in this article to retrieve the raindrop size distribution (RSD) parameters from X-band polarimetric weather radar data. In the IMT method, a forward mapping database from three parameters of a gamma-type RSD to polarimetric radar variables is first built based on the scattering simulations under ideal atmospheric conditions, and then an inverse mapping database is derived. In particular, given a fixed shape parameter ( $\mu $ ) of RSD, the intersection of horizontal reflectivity ( $Z_{\text {H}}$ ) and differential reflectivity ( $Z_{\text {DR}}$ ) contour lines is first obtained in the domain of total number concentration ( $N_{\text {T}}$ ) and median volume diameter (MVD) $D_{0}$ ; and the inverse mapping relationship between $Z_{H}$ and $Z_{\text {DR}}$ to $N_{T}$ and $D_{0}$ at a fixed $\mu $ value is derived to form a single layer of IMT. Then, the monotonic relationship between $\mu $ and the specific differential propagation phase shift ( $K_{\text {DP}}$ ) or backscatter differential phase ( $\delta _{\text {CO}}$ ) can aid in determining $\mu $ and a single layer of IMT. Thus, the inverse mapping database from polarimetric observations to the three gamma-type RSD parameters $\mu $ , $N_{\text {T}}$ , and $D_{0}$ can be established. Demonstration studies during a convective rainfall event and a large-scale rainfall event which occurred in northeastern China are carried out to examine the performance of this IMT method compared to a constrained-gamma (C-G) method that uses empirical relations between RSD parameters. The results show that the IMT method has a better performance in the convective case and similar performance in the large-scale continuous rainfall case.

An inverse model‐based multiobjective estimation of distribution algorithm using Random‐Forest variable importance methods

AbstractMost existing methods of multiobjective estimation of distributed algorithms apply the estimation of distribution of the Pareto‐solution on the decision space during the search and little work has proposed on making a regression‐model for representing the final solution set. Some inverse‐model‐based approaches were reported, such as inversed‐model of multiobjective evolutionary algorithm (IM‐MOEA), where an inverse functional mapping from Pareto‐Front to Pareto‐solution is constructed on nondominated solutions based on Gaussian process and random grouping technique. But some of the effective inverse models, during this process, may be removed. This paper proposes an inversed‐model based on random forest framework. The main idea is to apply the process of random forest variable importance that determines some of the best assignment of decision variables (xn) to objective functions (fm) for constructing Gaussian process in inversed‐models that map all nondominated solutions from the objective space to the decision space. In this work, three approaches have been used: classical permutation, Naïve testing approach, and novel permutation variable importance. The proposed algorithm has been tested on the benchmark test suite for evolutionary algorithms [modified Deb K, Thiele L, Laumanns M, Zitzler E (DTLZ) and Walking Fish Group (WFG)] and indicates that the proposed method is a competitive and promising approach.

RIS-GAN: Explore Residual and Illumination with Generative Adversarial Networks for Shadow Removal

Residual images and illumination estimation have been proved very helpful in image enhancement. In this paper, we propose a general and novel framework RIS-GAN which explores residual and illumination with Generative Adversarial Networks for shadow removal. Combined with the coarse shadow-removal image, the estimated negative residual images and inverse illumination maps can be used to generate indirect shadow-removal images to refine the coarse shadow-removal result to the fine shadow-free image in a coarse-to-fine fashion. Three discriminators are designed to distinguish whether the predicted negative residual images, shadow-removal images, and the inverse illumination maps are real or fake jointly compared with the corresponding ground-truth information. To our best knowledge, we are the first one to explore residual and illumination for shadow removal. We evaluate our proposed method on two benchmark datasets, i.e., SRD and ISTD, and the extensive experiments demonstrate that our proposed method achieves the superior performance to state-of-the-arts, although we have no particular shadow-aware components designed in our generators.

Attosecond pulse retrieval from noisy streaking traces with conditional variational generative network

Accurate characterization of an attosecond pulse from streaking trace is an indispensable step in studying the ultrafast electron dynamics on the attosecond scale. Conventional attosecond pulse retrieval methods face two major challenges: the ability to incorporate a complete physics model of the streaking process, and the ability to model the uncertainty of pulse reconstruction in the presence of noise. Here we propose a pulse retrieval method based on conditional variational generative network (CVGN) that can address both demands. Instead of learning the inverse mapping from a streaking trace to a pulse profile, the CVGN models the distribution of the pulse profile conditioned on a given streaking trace measurement, and is thus capable of assessing the uncertainty of the retrieved pulses. This capability is highly desirable for low-photon level measurement, which is typical in attosecond streaking experiments in the water window X-ray range. In addition, the proposed scheme incorporates a refined physics model that considers the Coulomb-laser coupling and photoelectron angular distribution in streaking trace generation. CVGN pulse retrievals under various simulated noise levels and experimental measurement have been demonstrated. The results showed high pulse reconstruction consistency for streaking traces when peak signal-to-noise ratio (SNR) exceeds 6, which could serve as a reference for future learning-based attosecond pulse retrieval.

SOLAR-GP: Sparse Online Locally Adaptive Regression Using Gaussian Processes for Bayesian Robot Model Learning and Control

Machine learning methods have been widely used in robot control to learn inverse mappings. These methods are used to capture the entire non-linearities and non-idealities of a system that make geometric or phenomenological modeling difficult. Most methods employ some form of off-line or batch learning where training may be performed prior to a task, or in an intermittent manner, respectively. These strategies are generally unsuitable for teleoperation, where commands and sensor data are received in sequential streams and models must be learned on-the-fly. We combine sparse, local, and streaming methods to form Sparse Online Locally Adaptive Regression using Gaussian Processes (SOLAR–GP), which trains streaming data on localized sparse Gaussian Process models and infers a weighted local function mapping of the robot sensor states to joint states. The resultant prediction of the teleoperation command is used for joint control. The algorithm was adapted to perform on arbitrary link manipulators including the Baxter robot, where modifications to the algorithm are made to run training and prediction in parallel so as to keep consistent, high-frequency control loop rates. This framework allows for a user-defined cap on complexity of generated local models while retaining information on older regions of the explored state-space.

Mappings with finite length distortion and prime ends on Riemann surfaces

The present paper is a continuation of our research that was devoted to the theory of the boundary behavior of mappings in the Sobolev classes (mappings with generalized derivatives) on Riemann surfaces. Here we develop the theory of the boundary behavior of the mappings in the class of FLD (mappings with finite length distortion) first introduced for the Euclidean spaces in the article of Martio-Ryazanov-Srebro-Yakubov at 2004 and then included in the known book of these authors at 2009 on the modern mapping theory. As was shown in the recent papers of Kovtonyuk-Petkov-Ryazanov at 2017, such mappings, generally speaking, are not mappings in the Sobolev classes, because their first partial derivatives can be not locally integrable. At the same time, this class is a natural generalization of the well-known significant classes of isometries and quasiisometries. We prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extensions to the boundary of the mappings with finite length distortion between domains on Riemann surfaces by Caratheodory prime ends. The criterion for the continuous extension of the inverse mapping to the boundary is turned out to be the very simple condition on the integrability of the dilatations in the first power. The criteria for the continuous extension of the direct mappings to the boundary have a much more refined nature. One of such criteria is the existence of a majorant for the dilatation in the class of functions with finite mean oscillation, i.e., having a finite mean deviation from its mean value over infinitesimal disks centered at boundary points. As consequences, the corresponding criteria for a homeomorphic extension of mappings with finite length distortion to the closures of domains by Caratheodory prime ends are obtained.

On the Equicontinuity of Families of Inverse Mappings of Riemannian Manifolds

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

Determining Roe and Metz model parameters for simulating multireader multicase confidence-of-disease rating data based on real-data or conjectured Obuchowski-Rockette parameter estimates.

The most frequently used model for simulating MRMC data that emulate confidence-of-disease ratings from diagnostic imaging studies has been the Roe and Metz model, proposed in 1997. The RM model generates continuous confidence-of-diseases ratings based on an underlying equal-variance binormal model for each reader, with the separation between the normal and abnormal rating distributions varying across readers. A problem with the RM model is that the parameters are expressed in terms of the rating distributions, as opposed to the reader performance outcomes. Because MRMC analysis results are almost always expressed in terms of the reader performance outcomes, and not in terms of the rating data distributions, it has been difficult to assess how similar the simulated data are to MRMC data encountered in practice. To remedy this situation, recently Hillis (in 2018) derived formulas expressing parameters that describe the distribution of empirical AUC outcomes computed from RM simulated data as functions of the RM parameters. An examination of these values revealed several problems with the realism of the simulated data. This paper continues that work by providing the inverse mapping, i.e., by deriving an algorithm that expresses the RM parameters as functions of the AUC empirical distribution parameters. This result will enable the creation of a recalibrated RM model that more closely emulates real-data studies.

Involutions, obstructions and mirror symmetry

Consider a Maslov zero Lagrangian submanifold diffeomorphic to a Lie group on which an anti-symplectic involution acts by the inverse map of the group. We show that the Fukaya A∞ endomorphism algebra of such a Lagrangian is quasi-isomorphic to its de Rham cohomology tensored with the Novikov field. In particular, it is unobstructed, formal, and its Floer and de Rham cohomologies coincide. Our result implies that the smooth fibers of a large class of singular Lagrangian fibrations are unobstructed and their Floer and de Rham cohomologies coincide. This is a step in the SYZ and family Floer cohomology approaches to mirror symmetry.More generally, our result continues to hold if the Lagrangian has cohomology the free graded algebra on a graded vector space V concentrated in odd degree, and the anti-symplectic involution acts on the cohomology of the Lagrangian by the induced map of negative the identity on V. It suffices for the Maslov class to vanish modulo 4.

Deep learning-based attenuation correction in the absence of structural information for whole-body positron emission tomography imaging

Deriving accurate structural maps for attenuation correction (AC) of whole-body positron emission tomography (PET) remains challenging. Common problems include truncation, inter-scan motion, and erroneous transformation of structural voxel-intensities to PET µ-map values (e.g. modality artifacts, implanted devices, or contrast agents). This work presents a deep learning-based attenuation correction (DL-AC) method to generate attenuation corrected PET (AC PET) from non-attenuation corrected PET (NAC PET) images for whole-body PET imaging, without the use of structural information. 3D patch-based cycle-consistent generative adversarial networks (CycleGAN) is introduced to include NAC-PET-to-AC-PET mapping and inverse mapping from AC PET to NAC PET, which constrains NAC-PET-to-AC-PET mapping to be closer to one-to-one mapping. Since NAC PET images share similar anatomical structures to the AC PET image but lack contrast information, residual blocks, which aim to learn the differences between NAC PET and AC PET, are used to construct generators of CycleGAN. After training, patches from NAC PET images were fed into NAC-PET-to-AC-PET mapping to generate DL-AC PET patches. DL-AC PET image was then reconstructed through patch fusion. We conducted a retrospective study on 55 datasets of whole-body PET/CT scans to evaluate the proposed method. In comparing DL-AC PET with original AC PET, average mean error (ME) and normalized mean square error (NMSE) of the whole-body were 0.62% ± 1.26% and 0.72% ± 0.34%. The average intensity changes measured on sequential PET images with AC and DL-AC on both normal tissues and lesions differ less than 3%. There was no significant difference of the intensity changes between AC and DL-AC PET, which demonstrate DL-AC PET images generated by the proposed DL-AC method can reach a same level to that of original AC PET images. The method demonstrates excellent quantification accuracy and reliability and is applicable to PET data collected on a single PET scanner or hybrid platform with computed tomography (PET/CT) or magnetic resonance imaging (PET/MRI).

Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C

An explicit isomorphism between the R-matrix and Drinfeld presentations of the quantum affine algebra in type A was given by Ding and Frenkel [Commun. Math. Phys. 156, 277–300 (1993)]. We show that this result can be extended to types B, C, and D and give a detailed construction for type C in this paper. In all classical types, the Gauss decomposition of the generator matrix in the R-matrix presentation yields the Drinfeld generators. To prove that the resulting map is an isomorphism, we follow the work of Frenkel and Mukhin [Sel. Math. 8, 537–635 (2002)] in type A and employ the universal R-matrix to construct the inverse map. A key role in our construction is played by a homomorphism theorem, which relates the quantum affine algebra of rank n − 1 in the R-matrix presentation with a subalgebra of the corresponding algebra of rank n of the same type.

Sketch to Photo Conversion using Cycle-Consistent Adversarial Networks

It is proposed to use the cycle-consistent adversarial network as a way to convert images of sketches to images of photos. The network learns to perform the mapping from the domain of sketches to the domain of photos and due to its architecture also learns the inverse mapping from the domain of photos to the domain of sketches. The network converts sketches to photos by reducing a weighted sum of the validity, reconstruction and identity losses. The advantage of using a cycle-consistent adversarial network over other network architectures is that it is not mandatory to have aligned image pairs as its training set and works in an unpaired setting.

Parallel manipulator domains of singularity free functionality

A mechanics-based parallel manipulator formulation with mechanism generalized coordinates, kinematic constraints, input coordinates, and output coordinates is employed to account for singularities that conventional input-output models cannot represent. Criteria are presented at the configuration level that assure local existence of differentiable forward and inverse kinematic mappings. Basic results of differential topology are used to extend local kinematic relationships to singularity free, path connected, maximal domains of functionality, on which reliable manipulator planning and control may be implemented. It is shown that any trajectory in manipulator configuration space between points in distinct domains of functionality must encounter a singularity. Methods are presented that define domains of functionality, using only linear algebra and multivariable calculus for implementation, and illustrated with three parallel manipulators of varying levels of complexity. The first example is a simple manipulator that demonstrates concepts. The second defines 16 domains of functionality in a seven-dimensional configuration space. The third is a construction earth moving manipulator, for which maximal domains of functionality and more conservative domains with input bounds that uniformly avoid singularities are presented. Communicated by Bogdan Gavrea.

An Inverse Mapping Theorem in Fréchet-Montel Spaces

Influenced by a recent note by M. Ivanov and N. Zlateva, we prove a statement in the style of Nash-Moser-Ekeland theorem for mappings from a Frechet-Montel space with values in any Frechet space (not necessarily standard). The mapping under consideration is supposed to be continuous and directionally differentiable (in particular Gateaux differentiable) with the derivative having a right inverse. We also consider an approximation by a graphical derivative and by a linear operator in the spirit of Graves’ theorem. Finally, we derive corollaries of the abstract results in finite dimensions. We obtain, in particular, sufficient conditions for the directional semiregularity of a mapping defined on a (locally) convex compact set in directions from a locally conic set; and also conditions guaranteeing that the nonlinear image of a convex set contains a prescribed ordered interval.

RST invariant watermarking technique for vector map based on LCA-transform

The dangers of copyright protection can impact 2D vector maps, having a knock-on effect on the use of vector data. To achieve invariance property, uniform RST (rotation, scaling and translation) and disguising the digital vector map’s information by implementing distortion control, is all done by using watermarking schemes. Convert an original map, then engrain the watermark. An LCA algorithm is used in this study, as a newly proposed way to protect the vector maps under copyright. The procedure is operated in this order: 1) use an original map, altered by the LCA algorithm, 2) use the coefficient of the transformation to engrain the watermark, inserting the resulting frequency into the LSB wave, 3) the watermarked map is acquired by using the inverse LCA map transformation. Further investigations discovered that the necessary standards of fidelity and invisibility can be achieved using this technique. This procedure also gives out numerous frequency domains for digital watermarking; as well as being resilient to signal and geometric invasions.

Multi-Channel Deep Networks for Block-Based Image Compressive Sensing

Incorporating deep neural networks in image compressive sensing (CS) receives intensive attentions in multimedia technology and applications recently. As deep network approaches learn the inverse mapping directly from the CS measurements, the reconstruction speed is significantly faster than the conventional CS algorithms. However, for existing network based approaches, a CS sampling procedure has to map a separate network model. This may potentially degrade the performance of image CS with block-wise sampling because of blocking artifacts, especially when multiple sampling rates are assigned to different blocks within an image. In this paper, we develop a multichannel deep network for block-based image CS by exploiting inter-block correlation with performance significantly exceeding the current state-of-the-art methods. The significant performance improvement is attributed to block-wise approximation but full image removal of blocking artifacts. Specifically, with our multichannel structure, the image blocks with a variety of sampling rates can be reconstructed in a single model. The initially reconstructed blocks are then capable of being reassembled into a full image to improve the recovered images by unrolling a hand-designed block based CS recovery algorithm. Experimental results demonstrate that the proposed method outperforms the state-of-the-art CS methods by a large margin in terms of objective metrics and subjective visual image quality. Our source codes are available at https://github.com/siwangzhou/DeepBCS.